Question

A disc jockey has 20 songs to choose from and can only play 8 in the next half hour. how many different playlists are possible?

Answer 1

This problem is a combination problem since it did not indicate that there is a specified order of songs to be played. The type of combination problem is without repetition. Thus the working equation would be n!/r!(n-r)! wherein n is the total number of songs to choose from and r is the number of songs you can choose at a given time. The answer would be 125970.

Answer 2

Answer: 125970

Explanation:

The number of combinations of n things taken r at a time is given by :-

`^nC_r=(n!)/(r!(n-r)!)`

Similarly , the number of combinations of 20 songs taken 8 at a time is given by :-

`^(20)C_8=(20!)/(8!(20-8)!)\\\\=(20*19*18*17*16*15*14*13*12!)/(8*7*6*5*4*3*2\timews12!)\\\\=125970`

Hence, the number of different playlists are possible= 125970